LMFDB - Embedded newform 187.2.e.a.166.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(89,187)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("187.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			166.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	187.166
Dual form			187.2.e.a.89.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +(-2.41421 - 2.41421i) q^{3} -2.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(4.82843 - 4.82843i) q^{6} +(-0.707107 + 0.707107i) q^{7} +8.65685i q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +(-2.41421 - 2.41421i) q^{3} -2.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(4.82843 - 4.82843i) q^{6} +(-0.707107 + 0.707107i) q^{7} +8.65685i q^{9} +(-4.00000 + 4.00000i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(4.82843 + 4.82843i) q^{12} -0.585786 q^{13} +(-1.41421 - 1.41421i) q^{14} -9.65685i q^{15} -4.00000 q^{16} +(2.12132 + 3.53553i) q^{17} -17.3137 q^{18} +5.41421i q^{19} +(-4.00000 - 4.00000i) q^{20} +3.41421 q^{21} +(-1.41421 - 1.41421i) q^{22} +(3.00000 - 3.00000i) q^{23} +3.00000i q^{25} -1.17157i q^{26} +(13.6569 - 13.6569i) q^{27} +(1.41421 - 1.41421i) q^{28} +(1.29289 + 1.29289i) q^{29} +19.3137 q^{30} +(0.828427 + 0.828427i) q^{31} -8.00000i q^{32} +3.41421 q^{33} +(-7.07107 + 4.24264i) q^{34} -2.82843 q^{35} -17.3137i q^{36} +(-4.65685 - 4.65685i) q^{37} -10.8284 q^{38} +(1.41421 + 1.41421i) q^{39} +(3.53553 - 3.53553i) q^{41} +6.82843i q^{42} -2.58579i q^{43} +(1.41421 - 1.41421i) q^{44} +(-17.3137 + 17.3137i) q^{45} +(6.00000 + 6.00000i) q^{46} -5.48528 q^{47} +(9.65685 + 9.65685i) q^{48} +6.00000i q^{49} -6.00000 q^{50} +(3.41421 - 13.6569i) q^{51} +1.17157 q^{52} -13.4853i q^{53} +(27.3137 + 27.3137i) q^{54} -2.82843 q^{55} +(13.0711 - 13.0711i) q^{57} +(-2.58579 + 2.58579i) q^{58} +6.65685i q^{59} +19.3137i q^{60} +(0.828427 - 0.828427i) q^{61} +(-1.65685 + 1.65685i) q^{62} +(-6.12132 - 6.12132i) q^{63} +8.00000 q^{64} +(-1.17157 - 1.17157i) q^{65} +6.82843i q^{66} +1.00000 q^{67} +(-4.24264 - 7.07107i) q^{68} -14.4853 q^{69} -5.65685i q^{70} +(3.07107 + 3.07107i) q^{71} +(9.77817 + 9.77817i) q^{73} +(9.31371 - 9.31371i) q^{74} +(7.24264 - 7.24264i) q^{75} -10.8284i q^{76} -1.00000i q^{77} +(-2.82843 + 2.82843i) q^{78} +(6.24264 - 6.24264i) q^{79} +(-8.00000 - 8.00000i) q^{80} -39.9706 q^{81} +(7.07107 + 7.07107i) q^{82} -0.828427i q^{83} -6.82843 q^{84} +(-2.82843 + 11.3137i) q^{85} +5.17157 q^{86} -6.24264i q^{87} +3.82843 q^{89} +(-34.6274 - 34.6274i) q^{90} +(0.414214 - 0.414214i) q^{91} +(-6.00000 + 6.00000i) q^{92} -4.00000i q^{93} -10.9706i q^{94} +(-10.8284 + 10.8284i) q^{95} +(-19.3137 + 19.3137i) q^{96} +(-2.58579 - 2.58579i) q^{97} -12.0000 q^{98} +(-6.12132 - 6.12132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) $ 4 * q - 4 * q^3 - 8 * q^4 + 8 * q^5 + 8 * q^6	$ 4 q - 4 q^{3} - 8 q^{4} + 8 q^{5} + 8 q^{6} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 16 q^{16} - 24 q^{18} - 16 q^{20} + 8 q^{21} + 12 q^{23} + 32 q^{27} + 8 q^{29} + 32 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{37} - 32 q^{38} - 24 q^{45} + 24 q^{46} + 12 q^{47} + 16 q^{48} - 24 q^{50} + 8 q^{51} + 16 q^{52} + 64 q^{54} + 24 q^{57} - 16 q^{58} - 8 q^{61} + 16 q^{62} - 16 q^{63} + 32 q^{64} - 16 q^{65} + 4 q^{67} - 24 q^{69} - 16 q^{71} + 8 q^{73} - 8 q^{74} + 12 q^{75} + 8 q^{79} - 32 q^{80} - 92 q^{81} - 16 q^{84} + 32 q^{86} + 4 q^{89} - 48 q^{90} - 4 q^{91} - 24 q^{92} - 32 q^{95} - 32 q^{96} - 16 q^{97} - 48 q^{98} - 16 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 8 * q^4 + 8 * q^5 + 8 * q^6 - 16 * q^10 + 8 * q^12 - 8 * q^13 - 16 * q^16 - 24 * q^18 - 16 * q^20 + 8 * q^21 + 12 * q^23 + 32 * q^27 + 8 * q^29 + 32 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^37 - 32 * q^38 - 24 * q^45 + 24 * q^46 + 12 * q^47 + 16 * q^48 - 24 * q^50 + 8 * q^51 + 16 * q^52 + 64 * q^54 + 24 * q^57 - 16 * q^58 - 8 * q^61 + 16 * q^62 - 16 * q^63 + 32 * q^64 - 16 * q^65 + 4 * q^67 - 24 * q^69 - 16 * q^71 + 8 * q^73 - 8 * q^74 + 12 * q^75 + 8 * q^79 - 32 * q^80 - 92 * q^81 - 16 * q^84 + 32 * q^86 + 4 * q^89 - 48 * q^90 - 4 * q^91 - 24 * q^92 - 32 * q^95 - 32 * q^96 - 16 * q^97 - 48 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.00000i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$2$			2.00000i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$3$	−2.41421	−	2.41421i	−1.39385	−	1.39385i	−0.816497	−	0.577350i	$-0.804087\pi$
$3$	−2.41421	−	2.41421i	−1.39385	−	1.39385i	−0.577350	−	0.816497i	$-0.695913\pi$
$4$	−2.00000			−1.00000
$5$	2.00000	+	2.00000i	0.894427	+	0.894427i	0.994936	−	0.100509i	$-0.0320471\pi$
$5$	2.00000	+	2.00000i	0.894427	+	0.894427i	−0.100509	+	0.994936i	$0.532047\pi$
$6$	4.82843	−	4.82843i	1.97120	−	1.97120i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i	−0.827996	−	0.560734i	$-0.810519\pi$
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i	0.560734	+	0.827996i	$0.310519\pi$
$8$		0			0
$9$			8.65685i			2.88562i
$10$	−4.00000	+	4.00000i	−1.26491	+	1.26491i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	4.82843	+	4.82843i	1.39385	+	1.39385i
$13$	−0.585786			−0.162468			−0.0812340	−	0.996695i	$-0.525886\pi$
$13$	−0.585786			−0.162468			−0.0812340	+	0.996695i	$0.525886\pi$
$14$	−1.41421	−	1.41421i	−0.377964	−	0.377964i
$15$		−	9.65685i		−	2.49339i
$16$	−4.00000			−1.00000
$17$	2.12132	+	3.53553i	0.514496	+	0.857493i
$17$	2.12132	+	3.53553i	0.514496	+	0.857493i
$18$	−17.3137			−4.08088
$19$			5.41421i			1.24211i	0.783769	+	0.621053i	$0.213295\pi$
$19$			5.41421i			1.24211i	−0.783769	+	0.621053i	$0.786705\pi$
$20$	−4.00000	−	4.00000i	−0.894427	−	0.894427i
$21$	3.41421			0.745042
$22$	−1.41421	−	1.41421i	−0.301511	−	0.301511i
$23$	3.00000	−	3.00000i	0.625543	−	0.625543i	−0.321400	−	0.946943i	$-0.604153\pi$
$23$	3.00000	−	3.00000i	0.625543	−	0.625543i	0.946943	+	0.321400i	$0.104153\pi$
$24$		0			0
$25$			3.00000i			0.600000i
$26$		−	1.17157i		−	0.229764i
$27$	13.6569	−	13.6569i	2.62826	−	2.62826i
$28$	1.41421	−	1.41421i	0.267261	−	0.267261i
$29$	1.29289	+	1.29289i	0.240084	+	0.240084i	0.816885	−	0.576801i	$-0.195699\pi$
$29$	1.29289	+	1.29289i	0.240084	+	0.240084i	−0.576801	+	0.816885i	$0.695699\pi$
$30$	19.3137			3.52618
$31$	0.828427	+	0.828427i	0.148790	+	0.148790i	0.777577	−	0.628787i	$-0.216448\pi$
$31$	0.828427	+	0.828427i	0.148790	+	0.148790i	−0.628787	+	0.777577i	$0.716448\pi$
$32$		−	8.00000i		−	1.41421i
$33$	3.41421			0.594338
$34$	−7.07107	+	4.24264i	−1.21268	+	0.727607i
$35$	−2.82843			−0.478091
$36$		−	17.3137i		−	2.88562i
$37$	−4.65685	−	4.65685i	−0.765582	−	0.765582i	0.211743	−	0.977325i	$-0.432086\pi$
$37$	−4.65685	−	4.65685i	−0.765582	−	0.765582i	−0.977325	+	0.211743i	$0.932086\pi$
$38$	−10.8284			−1.75660
$39$	1.41421	+	1.41421i	0.226455	+	0.226455i
$40$		0			0
$41$	3.53553	−	3.53553i	0.552158	−	0.552158i	−0.374905	−	0.927063i	$-0.622325\pi$
$41$	3.53553	−	3.53553i	0.552158	−	0.552158i	0.927063	+	0.374905i	$0.122325\pi$
$42$			6.82843i			1.05365i
$43$		−	2.58579i		−	0.394329i	−0.980370	−	0.197164i	$-0.936827\pi$
$43$		−	2.58579i		−	0.394329i	0.980370	−	0.197164i	$-0.0631733\pi$
$44$	1.41421	−	1.41421i	0.213201	−	0.213201i
$45$	−17.3137	+	17.3137i	−2.58098	+	2.58098i
$46$	6.00000	+	6.00000i	0.884652	+	0.884652i
$47$	−5.48528			−0.800111			−0.400055	−	0.916491i	$-0.631009\pi$
$47$	−5.48528			−0.800111			−0.400055	+	0.916491i	$0.631009\pi$
$48$	9.65685	+	9.65685i	1.39385	+	1.39385i
$49$			6.00000i			0.857143i
$50$	−6.00000			−0.848528
$51$	3.41421	−	13.6569i	0.478086	−	1.91234i
$52$	1.17157			0.162468
$53$		−	13.4853i		−	1.85235i	−0.377099	−	0.926173i	$-0.623078\pi$
$53$		−	13.4853i		−	1.85235i	0.377099	−	0.926173i	$-0.376922\pi$
$54$	27.3137	+	27.3137i	3.71692	+	3.71692i
$55$	−2.82843			−0.381385
$56$		0			0
$57$	13.0711	−	13.0711i	1.73131	−	1.73131i
$58$	−2.58579	+	2.58579i	−0.339530	+	0.339530i
$59$			6.65685i			0.866649i	0.901238	+	0.433324i	$0.142660\pi$
$59$			6.65685i			0.866649i	−0.901238	+	0.433324i	$0.857340\pi$
$60$			19.3137i			2.49339i
$61$	0.828427	−	0.828427i	0.106069	−	0.106069i	−0.652081	−	0.758150i	$-0.726104\pi$
$61$	0.828427	−	0.828427i	0.106069	−	0.106069i	0.758150	+	0.652081i	$0.226104\pi$
$62$	−1.65685	+	1.65685i	−0.210421	+	0.210421i
$63$	−6.12132	−	6.12132i	−0.771214	−	0.771214i
$64$	8.00000			1.00000
$65$	−1.17157	−	1.17157i	−0.145316	−	0.145316i
$66$			6.82843i			0.840521i
$67$	1.00000			0.122169			0.0610847	−	0.998133i	$-0.480544\pi$
$67$	1.00000			0.122169			0.0610847	+	0.998133i	$0.480544\pi$
$68$	−4.24264	−	7.07107i	−0.514496	−	0.857493i
$69$	−14.4853			−1.74382
$70$		−	5.65685i		−	0.676123i
$71$	3.07107	+	3.07107i	0.364469	+	0.364469i	0.865455	−	0.500986i	$-0.167029\pi$
$71$	3.07107	+	3.07107i	0.364469	+	0.364469i	−0.500986	+	0.865455i	$0.667029\pi$
$72$		0			0
$73$	9.77817	+	9.77817i	1.14445	+	1.14445i	0.987627	+	0.156822i	$0.0501249\pi$
$73$	9.77817	+	9.77817i	1.14445	+	1.14445i	0.156822	+	0.987627i	$0.449875\pi$
$74$	9.31371	−	9.31371i	1.08270	−	1.08270i
$75$	7.24264	−	7.24264i	0.836308	−	0.836308i
$76$		−	10.8284i		−	1.24211i
$77$		−	1.00000i		−	0.113961i
$78$	−2.82843	+	2.82843i	−0.320256	+	0.320256i
$79$	6.24264	−	6.24264i	0.702352	−	0.702352i	−0.262563	−	0.964915i	$-0.584568\pi$
$79$	6.24264	−	6.24264i	0.702352	−	0.702352i	0.964915	+	0.262563i	$0.0845677\pi$
$80$	−8.00000	−	8.00000i	−0.894427	−	0.894427i
$81$	−39.9706			−4.44117
$82$	7.07107	+	7.07107i	0.780869	+	0.780869i
$83$		−	0.828427i		−	0.0909317i	−0.998966	−	0.0454658i	$-0.985523\pi$
$83$		−	0.828427i		−	0.0909317i	0.998966	−	0.0454658i	$-0.0144772\pi$
$84$	−6.82843			−0.745042
$85$	−2.82843	+	11.3137i	−0.306786	+	1.22714i
$86$	5.17157			0.557665
$87$		−	6.24264i		−	0.669281i
$88$		0			0
$89$	3.82843			0.405812			0.202906	−	0.979198i	$-0.434961\pi$
$89$	3.82843			0.405812			0.202906	+	0.979198i	$0.434961\pi$
$90$	−34.6274	−	34.6274i	−3.65005	−	3.65005i
$91$	0.414214	−	0.414214i	0.0434214	−	0.0434214i
$92$	−6.00000	+	6.00000i	−0.625543	+	0.625543i
$93$		−	4.00000i		−	0.414781i
$94$		−	10.9706i		−	1.13153i
$95$	−10.8284	+	10.8284i	−1.11097	+	1.11097i
$96$	−19.3137	+	19.3137i	−1.97120	+	1.97120i
$97$	−2.58579	−	2.58579i	−0.262547	−	0.262547i	0.563541	−	0.826088i	$-0.309439\pi$
$97$	−2.58579	−	2.58579i	−0.262547	−	0.262547i	−0.826088	+	0.563541i	$0.809439\pi$
$98$	−12.0000			−1.21218
$99$	−6.12132	−	6.12132i	−0.615216	−	0.615216i
$100$		−	6.00000i		−	0.600000i
$101$	14.7279			1.46548			0.732742	−	0.680507i	$-0.238240\pi$
$101$	14.7279			1.46548			0.732742	+	0.680507i	$0.238240\pi$
$102$	27.3137	+	6.82843i	2.70446	+	0.676115i
$103$	5.34315			0.526476			0.263238	−	0.964731i	$-0.415210\pi$
$103$	5.34315			0.526476			0.263238	+	0.964731i	$0.415210\pi$
$104$		0			0
$105$	6.82843	+	6.82843i	0.666386	+	0.666386i
$106$	26.9706			2.61961
$107$	−7.53553	−	7.53553i	−0.728488	−	0.728488i	0.241831	−	0.970318i	$-0.422252\pi$
$107$	−7.53553	−	7.53553i	−0.728488	−	0.728488i	−0.970318	+	0.241831i	$0.922252\pi$
$108$	−27.3137	+	27.3137i	−2.62826	+	2.62826i
$109$	−1.05025	+	1.05025i	−0.100596	+	0.100596i	−0.755614	−	0.655018i	$-0.772661\pi$
$109$	−1.05025	+	1.05025i	−0.100596	+	0.100596i	0.655018	+	0.755614i	$0.272661\pi$
$110$		−	5.65685i		−	0.539360i
$111$			22.4853i			2.13421i
$112$	2.82843	−	2.82843i	0.267261	−	0.267261i
$113$	−2.58579	+	2.58579i	−0.243250	+	0.243250i	−0.818193	−	0.574943i	$-0.805024\pi$
$113$	−2.58579	+	2.58579i	−0.243250	+	0.243250i	0.574943	+	0.818193i	$0.305024\pi$
$114$	26.1421	+	26.1421i	2.44844	+	2.44844i
$115$	12.0000			1.11901
$116$	−2.58579	−	2.58579i	−0.240084	−	0.240084i
$117$		−	5.07107i		−	0.468820i
$118$	−13.3137			−1.22563
$119$	−4.00000	−	1.00000i	−0.366679	−	0.0916698i
$120$		0			0
$121$		−	1.00000i		−	0.0909091i
$122$	1.65685	+	1.65685i	0.150005	+	0.150005i
$123$	−17.0711			−1.53925
$124$	−1.65685	−	1.65685i	−0.148790	−	0.148790i
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	12.2426	−	12.2426i	1.09066	−	1.09066i
$127$			14.2426i			1.26383i	0.775038	+	0.631915i	$0.217731\pi$
$127$			14.2426i			1.26383i	−0.775038	+	0.631915i	$0.782269\pi$
$128$		0			0
$129$	−6.24264	+	6.24264i	−0.549634	+	0.549634i
$130$	2.34315	−	2.34315i	0.205507	−	0.205507i
$131$	5.53553	+	5.53553i	0.483642	+	0.483642i	0.906293	−	0.422651i	$-0.138900\pi$
$131$	5.53553	+	5.53553i	0.483642	+	0.483642i	−0.422651	+	0.906293i	$0.638900\pi$
$132$	−6.82843			−0.594338
$133$	−3.82843	−	3.82843i	−0.331967	−	0.331967i
$134$			2.00000i			0.172774i
$135$	54.6274			4.70158
$136$		0			0
$137$	4.17157			0.356402			0.178201	−	0.983994i	$-0.442972\pi$
$137$	4.17157			0.356402			0.178201	+	0.983994i	$0.442972\pi$
$138$		−	28.9706i		−	2.46614i
$139$	−8.36396	−	8.36396i	−0.709422	−	0.709422i	0.256992	−	0.966414i	$-0.417269\pi$
$139$	−8.36396	−	8.36396i	−0.709422	−	0.709422i	−0.966414	+	0.256992i	$0.917269\pi$
$140$	5.65685			0.478091
$141$	13.2426	+	13.2426i	1.11523	+	1.11523i
$142$	−6.14214	+	6.14214i	−0.515437	+	0.515437i
$143$	0.414214	−	0.414214i	0.0346383	−	0.0346383i
$144$		−	34.6274i		−	2.88562i
$145$			5.17157i			0.429476i
$146$	−19.5563	+	19.5563i	−1.61849	+	1.61849i
$147$	14.4853	−	14.4853i	1.19473	−	1.19473i
$148$	9.31371	+	9.31371i	0.765582	+	0.765582i
$149$	11.7574			0.963200			0.481600	−	0.876391i	$-0.340056\pi$
$149$	11.7574			0.963200			0.481600	+	0.876391i	$0.340056\pi$
$150$	14.4853	+	14.4853i	1.18272	+	1.18272i
$151$			10.4853i			0.853280i	0.904422	+	0.426640i	$0.140303\pi$
$151$			10.4853i			0.853280i	−0.904422	+	0.426640i	$0.859697\pi$
$152$		0			0
$153$	−30.6066	+	18.3640i	−2.47440	+	1.48464i
$154$	2.00000			0.161165
$155$			3.31371i			0.266163i
$156$	−2.82843	−	2.82843i	−0.226455	−	0.226455i
$157$	2.31371			0.184654			0.0923270	−	0.995729i	$-0.470569\pi$
$157$	2.31371			0.184654			0.0923270	+	0.995729i	$0.470569\pi$
$158$	12.4853	+	12.4853i	0.993276	+	0.993276i
$159$	−32.5563	+	32.5563i	−2.58189	+	2.58189i
$160$	16.0000	−	16.0000i	1.26491	−	1.26491i
$161$			4.24264i			0.334367i
$162$		−	79.9411i		−	6.28077i
$163$	−5.00000	+	5.00000i	−0.391630	+	0.391630i	−0.875268	−	0.483638i	$-0.839315\pi$
$163$	−5.00000	+	5.00000i	−0.391630	+	0.391630i	0.483638	+	0.875268i	$0.339315\pi$
$164$	−7.07107	+	7.07107i	−0.552158	+	0.552158i
$165$	6.82843	+	6.82843i	0.531592	+	0.531592i
$166$	1.65685			0.128597
$167$	17.0711	+	17.0711i	1.32100	+	1.32100i	0.912968	+	0.408031i	$0.133784\pi$
$167$	17.0711	+	17.0711i	1.32100	+	1.32100i	0.408031	+	0.912968i	$0.366216\pi$
$168$		0			0
$169$	−12.6569			−0.973604
$170$	−22.6274	−	5.65685i	−1.73544	−	0.433861i
$171$	−46.8701			−3.58424
$172$			5.17157i			0.394329i
$173$	−4.12132	−	4.12132i	−0.313338	−	0.313338i	0.532863	−	0.846201i	$-0.321116\pi$
$173$	−4.12132	−	4.12132i	−0.313338	−	0.313338i	−0.846201	+	0.532863i	$0.821116\pi$
$174$	12.4853			0.946507
$175$	−2.12132	−	2.12132i	−0.160357	−	0.160357i
$176$	2.82843	−	2.82843i	0.213201	−	0.213201i
$177$	16.0711	−	16.0711i	1.20798	−	1.20798i
$178$			7.65685i			0.573905i
$179$		−	19.6274i		−	1.46702i	−0.679678	−	0.733511i	$-0.737880\pi$
$179$		−	19.6274i		−	1.46702i	0.679678	−	0.733511i	$-0.262120\pi$
$180$	34.6274	−	34.6274i	2.58098	−	2.58098i
$181$	1.07107	−	1.07107i	0.0796118	−	0.0796118i	−0.666180	−	0.745791i	$-0.732072\pi$
$181$	1.07107	−	1.07107i	0.0796118	−	0.0796118i	0.745791	+	0.666180i	$0.232072\pi$
$182$	0.828427	+	0.828427i	0.0614071	+	0.0614071i
$183$	−4.00000			−0.295689
$184$		0			0
$185$		−	18.6274i		−	1.36951i
$186$	8.00000			0.586588
$187$	−4.00000	−	1.00000i	−0.292509	−	0.0731272i
$188$	10.9706			0.800111
$189$			19.3137i			1.40487i
$190$	−21.6569	−	21.6569i	−1.57115	−	1.57115i
$191$	12.8284			0.928232			0.464116	−	0.885774i	$-0.346372\pi$
$191$	12.8284			0.928232			0.464116	+	0.885774i	$0.346372\pi$
$192$	−19.3137	−	19.3137i	−1.39385	−	1.39385i
$193$	14.8284	−	14.8284i	1.06737	−	1.06737i	0.0698135	−	0.997560i	$-0.477760\pi$
$193$	14.8284	−	14.8284i	1.06737	−	1.06737i	0.997560	−	0.0698135i	$-0.0222404\pi$
$194$	5.17157	−	5.17157i	0.371297	−	0.371297i
$195$			5.65685i			0.405096i
$196$		−	12.0000i		−	0.857143i
$197$	2.34315	−	2.34315i	0.166942	−	0.166942i	−0.618692	−	0.785634i	$-0.712337\pi$
$197$	2.34315	−	2.34315i	0.166942	−	0.166942i	0.785634	+	0.618692i	$0.212337\pi$
$198$	12.2426	−	12.2426i	0.870047	−	0.870047i
$199$	−12.5858	−	12.5858i	−0.892183	−	0.892183i	0.102546	−	0.994728i	$-0.467301\pi$
$199$	−12.5858	−	12.5858i	−0.892183	−	0.892183i	−0.994728	+	0.102546i	$0.967301\pi$
$200$		0			0
$201$	−2.41421	−	2.41421i	−0.170285	−	0.170285i
$202$			29.4558i			2.07251i
$203$	−1.82843			−0.128330
$204$	−6.82843	+	27.3137i	−0.478086	+	1.91234i
$205$	14.1421			0.987730
$206$			10.6863i			0.744549i
$207$	25.9706	+	25.9706i	1.80508	+	1.80508i
$208$	2.34315			0.162468
$209$	−3.82843	−	3.82843i	−0.264818	−	0.264818i
$210$	−13.6569	+	13.6569i	−0.942412	+	0.942412i
$211$	−6.36396	+	6.36396i	−0.438113	+	0.438113i	−0.891377	−	0.453263i	$-0.850260\pi$
$211$	−6.36396	+	6.36396i	−0.438113	+	0.438113i	0.453263	+	0.891377i	$0.350260\pi$
$212$			26.9706i			1.85235i
$213$		−	14.8284i		−	1.01603i
$214$	15.0711	−	15.0711i	1.03024	−	1.03024i
$215$	5.17157	−	5.17157i	0.352698	−	0.352698i
$216$		0			0
$217$	−1.17157			−0.0795315
$218$	−2.10051	−	2.10051i	−0.142264	−	0.142264i
$219$		−	47.2132i		−	3.19037i
$220$	5.65685			0.381385
$221$	−1.24264	−	2.07107i	−0.0835891	−	0.139315i
$222$	−44.9706			−3.01823
$223$		−	6.00000i		−	0.401790i	−0.979613	−	0.200895i	$-0.935615\pi$
$223$		−	6.00000i		−	0.401790i	0.979613	−	0.200895i	$-0.0643850\pi$
$224$	5.65685	+	5.65685i	0.377964	+	0.377964i
$225$	−25.9706			−1.73137
$226$	−5.17157	−	5.17157i	−0.344008	−	0.344008i
$227$	5.77817	−	5.77817i	0.383511	−	0.383511i	−0.488854	−	0.872365i	$-0.662585\pi$
$227$	5.77817	−	5.77817i	0.383511	−	0.383511i	0.872365	+	0.488854i	$0.162585\pi$
$228$	−26.1421	+	26.1421i	−1.73131	+	1.73131i
$229$		−	6.65685i		−	0.439897i	−0.975511	−	0.219949i	$-0.929411\pi$
$229$		−	6.65685i		−	0.439897i	0.975511	−	0.219949i	$-0.0705890\pi$
$230$			24.0000i			1.58251i
$231$	−2.41421	+	2.41421i	−0.158844	+	0.158844i
$232$		0			0
$233$	−8.46447	−	8.46447i	−0.554526	−	0.554526i	0.373218	−	0.927744i	$-0.378254\pi$
$233$	−8.46447	−	8.46447i	−0.554526	−	0.554526i	−0.927744	+	0.373218i	$0.878254\pi$
$234$	10.1421			0.663012
$235$	−10.9706	−	10.9706i	−0.715641	−	0.715641i
$236$		−	13.3137i		−	0.866649i
$237$	−30.1421			−1.95794
$238$	2.00000	−	8.00000i	0.129641	−	0.518563i
$239$	10.9289			0.706934			0.353467	−	0.935447i	$-0.385003\pi$
$239$	10.9289			0.706934			0.353467	+	0.935447i	$0.385003\pi$
$240$			38.6274i			2.49339i
$241$	−17.4350	−	17.4350i	−1.12309	−	1.12309i	−0.991274	−	0.131815i	$-0.957920\pi$
$241$	−17.4350	−	17.4350i	−1.12309	−	1.12309i	−0.131815	−	0.991274i	$-0.542080\pi$
$242$	2.00000			0.128565
$243$	55.5269	+	55.5269i	3.56205	+	3.56205i
$244$	−1.65685	+	1.65685i	−0.106069	+	0.106069i
$245$	−12.0000	+	12.0000i	−0.766652	+	0.766652i
$246$		−	34.1421i		−	2.17682i
$247$		−	3.17157i		−	0.201802i
$248$		0			0
$249$	−2.00000	+	2.00000i	−0.126745	+	0.126745i
$250$	8.00000	+	8.00000i	0.505964	+	0.505964i
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$	12.2426	+	12.2426i	0.771214	+	0.771214i
$253$			4.24264i			0.266733i
$254$	−28.4853			−1.78733
$255$	34.1421	−	20.4853i	2.13806	−	1.28284i
$256$	16.0000			1.00000
$257$			27.4853i			1.71448i	0.514913	+	0.857242i	$0.327824\pi$
$257$			27.4853i			1.71448i	−0.514913	+	0.857242i	$0.672176\pi$
$258$	−12.4853	−	12.4853i	−0.777300	−	0.777300i
$259$	6.58579			0.409221
$260$	2.34315	+	2.34315i	0.145316	+	0.145316i
$261$	−11.1924	+	11.1924i	−0.692791	+	0.692791i
$262$	−11.0711	+	11.0711i	−0.683973	+	0.683973i
$263$			25.5563i			1.57587i	0.615757	+	0.787936i	$0.288850\pi$
$263$			25.5563i			1.57587i	−0.615757	+	0.787936i	$0.711150\pi$
$264$		0			0
$265$	26.9706	−	26.9706i	1.65679	−	1.65679i
$266$	7.65685	−	7.65685i	0.469472	−	0.469472i
$267$	−9.24264	−	9.24264i	−0.565640	−	0.565640i
$268$	−2.00000			−0.122169
$269$	1.92893	+	1.92893i	0.117609	+	0.117609i	0.763462	−	0.645853i	$-0.223498\pi$
$269$	1.92893	+	1.92893i	0.117609	+	0.117609i	−0.645853	+	0.763462i	$0.723498\pi$
$270$			109.255i			6.64904i
$271$	−6.68629			−0.406163			−0.203082	−	0.979162i	$-0.565096\pi$
$271$	−6.68629			−0.406163			−0.203082	+	0.979162i	$0.565096\pi$
$272$	−8.48528	−	14.1421i	−0.514496	−	0.857493i
$273$	−2.00000			−0.121046
$274$			8.34315i			0.504028i
$275$	−2.12132	−	2.12132i	−0.127920	−	0.127920i
$276$	28.9706			1.74382
$277$	−17.5355	−	17.5355i	−1.05361	−	1.05361i	−0.998479	−	0.0551289i	$-0.982443\pi$
$277$	−17.5355	−	17.5355i	−1.05361	−	1.05361i	−0.0551289	−	0.998479i	$-0.517557\pi$
$278$	16.7279	−	16.7279i	1.00327	−	1.00327i
$279$	−7.17157	+	7.17157i	−0.429351	+	0.429351i
$280$		0			0
$281$		−	0.485281i		−	0.0289495i	−0.999895	−	0.0144747i	$-0.995392\pi$
$281$		−	0.485281i		−	0.0289495i	0.999895	−	0.0144747i	$-0.00460761\pi$
$282$	−26.4853	+	26.4853i	−1.57718	+	1.57718i
$283$	13.0711	−	13.0711i	0.776994	−	0.776994i	−0.202324	−	0.979319i	$-0.564849\pi$
$283$	13.0711	−	13.0711i	0.776994	−	0.776994i	0.979319	+	0.202324i	$0.0648495\pi$
$284$	−6.14214	−	6.14214i	−0.364469	−	0.364469i
$285$	52.2843			3.09705
$286$	0.828427	+	0.828427i	0.0489859	+	0.0489859i
$287$			5.00000i			0.295141i
$288$	69.2548			4.08088
$289$	−8.00000	+	15.0000i	−0.470588	+	0.882353i
$290$	−10.3431			−0.607370
$291$			12.4853i			0.731900i
$292$	−19.5563	−	19.5563i	−1.14445	−	1.14445i
$293$	25.0711			1.46467			0.732334	−	0.680946i	$-0.238431\pi$
$293$	25.0711			1.46467			0.732334	+	0.680946i	$0.238431\pi$
$294$	28.9706	+	28.9706i	1.68960	+	1.68960i
$295$	−13.3137	+	13.3137i	−0.775154	+	0.775154i
$296$		0			0
$297$			19.3137i			1.12070i
$298$			23.5147i			1.36217i
$299$	−1.75736	+	1.75736i	−0.101631	+	0.101631i
$300$	−14.4853	+	14.4853i	−0.836308	+	0.836308i
$301$	1.82843	+	1.82843i	0.105389	+	0.105389i
$302$	−20.9706			−1.20672
$303$	−35.5563	−	35.5563i	−2.04266	−	2.04266i
$304$		−	21.6569i		−	1.24211i
$305$	3.31371			0.189742
$306$	−36.7279	−	61.2132i	−2.09960	−	3.49933i
$307$	−13.7574			−0.785174			−0.392587	−	0.919715i	$-0.628420\pi$
$307$	−13.7574			−0.785174			−0.392587	+	0.919715i	$0.628420\pi$
$308$			2.00000i			0.113961i
$309$	−12.8995	−	12.8995i	−0.733827	−	0.733827i
$310$	−6.62742			−0.376412
$311$	−9.65685	−	9.65685i	−0.547590	−	0.547590i	0.378153	−	0.925743i	$-0.376559\pi$
$311$	−9.65685	−	9.65685i	−0.547590	−	0.547590i	−0.925743	+	0.378153i	$0.876559\pi$
$312$		0			0
$313$	−7.58579	+	7.58579i	−0.428774	+	0.428774i	−0.888211	−	0.459437i	$-0.848051\pi$
$313$	−7.58579	+	7.58579i	−0.428774	+	0.428774i	0.459437	+	0.888211i	$0.348051\pi$
$314$			4.62742i			0.261140i
$315$		−	24.4853i		−	1.37959i
$316$	−12.4853	+	12.4853i	−0.702352	+	0.702352i
$317$	11.4142	−	11.4142i	0.641086	−	0.641086i	−0.309736	−	0.950822i	$-0.600241\pi$
$317$	11.4142	−	11.4142i	0.641086	−	0.641086i	0.950822	+	0.309736i	$0.100241\pi$
$318$	−65.1127	−	65.1127i	−3.65134	−	3.65134i
$319$	−1.82843			−0.102372
$320$	16.0000	+	16.0000i	0.894427	+	0.894427i
$321$			36.3848i			2.03080i
$322$	−8.48528			−0.472866
$323$	−19.1421	+	11.4853i	−1.06510	+	0.639058i
$324$	79.9411			4.44117
$325$		−	1.75736i		−	0.0974808i
$326$	−10.0000	−	10.0000i	−0.553849	−	0.553849i
$327$	5.07107			0.280431
$328$		0			0
$329$	3.87868	−	3.87868i	0.213839	−	0.213839i
$330$	−13.6569	+	13.6569i	−0.751785	+	0.751785i
$331$		−	0.343146i		−	0.0188610i	−0.999956	−	0.00943050i	$-0.996998\pi$
$331$		−	0.343146i		−	0.0188610i	0.999956	−	0.00943050i	$-0.00300187\pi$
$332$			1.65685i			0.0909317i
$333$	40.3137	−	40.3137i	2.20918	−	2.20918i
$334$	−34.1421	+	34.1421i	−1.86817	+	1.86817i
$335$	2.00000	+	2.00000i	0.109272	+	0.109272i
$336$	−13.6569			−0.745042
$337$	−10.2635	−	10.2635i	−0.559086	−	0.559086i	0.369961	−	0.929047i	$-0.379371\pi$
$337$	−10.2635	−	10.2635i	−0.559086	−	0.559086i	−0.929047	+	0.369961i	$0.879371\pi$
$338$		−	25.3137i		−	1.37688i
$339$	12.4853			0.678107
$340$	5.65685	−	22.6274i	0.306786	−	1.22714i
$341$	−1.17157			−0.0634442
$342$		−	93.7401i		−	5.06888i
$343$	−9.19239	−	9.19239i	−0.496342	−	0.496342i
$344$		0			0
$345$	−28.9706	−	28.9706i	−1.55972	−	1.55972i
$346$	8.24264	−	8.24264i	0.443127	−	0.443127i
$347$	−11.4350	+	11.4350i	−0.613865	+	0.613865i	−0.943951	−	0.330086i	$-0.892922\pi$
$347$	−11.4350	+	11.4350i	−0.613865	+	0.613865i	0.330086	+	0.943951i	$0.392922\pi$
$348$			12.4853i			0.669281i
$349$			23.6985i			1.26855i	0.773107	+	0.634275i	$0.218701\pi$
$349$			23.6985i			1.26855i	−0.773107	+	0.634275i	$0.781299\pi$
$350$	4.24264	−	4.24264i	0.226779	−	0.226779i
$351$	−8.00000	+	8.00000i	−0.427008	+	0.427008i
$352$	5.65685	+	5.65685i	0.301511	+	0.301511i
$353$	−17.8284			−0.948911			−0.474456	−	0.880279i	$-0.657355\pi$
$353$	−17.8284			−0.948911			−0.474456	+	0.880279i	$0.657355\pi$
$354$	32.1421	+	32.1421i	1.70834	+	1.70834i
$355$			12.2843i			0.651981i
$356$	−7.65685			−0.405812
$357$	7.24264	+	12.0711i	0.383321	+	0.638869i
$358$	39.2548			2.07468
$359$		−	3.85786i		−	0.203610i	−0.994804	−	0.101805i	$-0.967538\pi$
$359$		−	3.85786i		−	0.203610i	0.994804	−	0.101805i	$-0.0324618\pi$
$360$		0			0
$361$	−10.3137			−0.542827
$362$	2.14214	+	2.14214i	0.112588	+	0.112588i
$363$	−2.41421	+	2.41421i	−0.126713	+	0.126713i
$364$	−0.828427	+	0.828427i	−0.0434214	+	0.0434214i
$365$			39.1127i			2.04725i
$366$		−	8.00000i		−	0.418167i
$367$	−7.17157	+	7.17157i	−0.374353	+	0.374353i	−0.869060	−	0.494707i	$-0.835275\pi$
$367$	−7.17157	+	7.17157i	−0.374353	+	0.374353i	0.494707	+	0.869060i	$0.335275\pi$
$368$	−12.0000	+	12.0000i	−0.625543	+	0.625543i
$369$	30.6066	+	30.6066i	1.59332	+	1.59332i
$370$	37.2548			1.93679
$371$	9.53553	+	9.53553i	0.495060	+	0.495060i
$372$			8.00000i			0.414781i
$373$	3.27208			0.169422			0.0847109	−	0.996406i	$-0.473003\pi$
$373$	3.27208			0.169422			0.0847109	+	0.996406i	$0.473003\pi$
$374$	2.00000	−	8.00000i	0.103418	−	0.413670i
$375$	−19.3137			−0.997356
$376$		0			0
$377$	−0.757359	−	0.757359i	−0.0390060	−	0.0390060i
$378$	−38.6274			−1.98678
$379$	6.55635	+	6.55635i	0.336777	+	0.336777i	0.855153	−	0.518376i	$-0.173463\pi$
$379$	6.55635	+	6.55635i	0.336777	+	0.336777i	−0.518376	+	0.855153i	$0.673463\pi$
$380$	21.6569	−	21.6569i	1.11097	−	1.11097i
$381$	34.3848	−	34.3848i	1.76159	−	1.76159i
$382$			25.6569i			1.31272i
$383$		−	19.4558i		−	0.994147i	−0.867708	−	0.497074i	$-0.834408\pi$
$383$		−	19.4558i		−	0.994147i	0.867708	−	0.497074i	$-0.165592\pi$
$384$		0			0
$385$	2.00000	−	2.00000i	0.101929	−	0.101929i
$386$	29.6569	+	29.6569i	1.50949	+	1.50949i
$387$	22.3848			1.13788
$388$	5.17157	+	5.17157i	0.262547	+	0.262547i
$389$		−	9.00000i		−	0.456318i	−0.973624	−	0.228159i	$-0.926729\pi$
$389$		−	9.00000i		−	0.456318i	0.973624	−	0.228159i	$-0.0732706\pi$
$390$	−11.3137			−0.572892
$391$	16.9706	+	4.24264i	0.858238	+	0.214560i
$392$		0			0
$393$		−	26.7279i		−	1.34825i
$394$	4.68629	+	4.68629i	0.236092	+	0.236092i
$395$	24.9706			1.25641
$396$	12.2426	+	12.2426i	0.615216	+	0.615216i
$397$	−25.7279	+	25.7279i	−1.29125	+	1.29125i	−0.357232	+	0.934016i	$0.616279\pi$
$397$	−25.7279	+	25.7279i	−1.29125	+	1.29125i	−0.934016	+	0.357232i	$0.883721\pi$
$398$	25.1716	−	25.1716i	1.26174	−	1.26174i
$399$			18.4853i			0.925422i
$400$		−	12.0000i		−	0.600000i
$401$	8.48528	−	8.48528i	0.423735	−	0.423735i	−0.462753	−	0.886487i	$-0.653138\pi$
$401$	8.48528	−	8.48528i	0.423735	−	0.423735i	0.886487	+	0.462753i	$0.153138\pi$
$402$	4.82843	−	4.82843i	0.240820	−	0.240820i
$403$	−0.485281	−	0.485281i	−0.0241736	−	0.0241736i
$404$	−29.4558			−1.46548
$405$	−79.9411	−	79.9411i	−3.97231	−	3.97231i
$406$		−	3.65685i		−	0.181487i
$407$	6.58579			0.326445
$408$		0			0
$409$	−18.1421			−0.897071			−0.448535	−	0.893765i	$-0.648054\pi$
$409$	−18.1421			−0.897071			−0.448535	+	0.893765i	$0.648054\pi$
$410$			28.2843i			1.39686i
$411$	−10.0711	−	10.0711i	−0.496769	−	0.496769i
$412$	−10.6863			−0.526476
$413$	−4.70711	−	4.70711i	−0.231622	−	0.231622i
$414$	−51.9411	+	51.9411i	−2.55277	+	2.55277i
$415$	1.65685	−	1.65685i	0.0813318	−	0.0813318i
$416$			4.68629i			0.229764i
$417$			40.3848i			1.97765i
$418$	7.65685	−	7.65685i	0.374509	−	0.374509i
$419$	19.6569	−	19.6569i	0.960300	−	0.960300i	−0.0389413	−	0.999241i	$-0.512399\pi$
$419$	19.6569	−	19.6569i	0.960300	−	0.960300i	0.999241	+	0.0389413i	$0.0123985\pi$
$420$	−13.6569	−	13.6569i	−0.666386	−	0.666386i
$421$	2.31371			0.112763			0.0563816	−	0.998409i	$-0.482044\pi$
$421$	2.31371			0.112763			0.0563816	+	0.998409i	$0.482044\pi$
$422$	−12.7279	−	12.7279i	−0.619586	−	0.619586i
$423$		−	47.4853i		−	2.30881i
$424$		0			0
$425$	−10.6066	+	6.36396i	−0.514496	+	0.308697i
$426$	29.6569			1.43688
$427$			1.17157i			0.0566964i
$428$	15.0711	+	15.0711i	0.728488	+	0.728488i
$429$	−2.00000			−0.0965609
$430$	10.3431	+	10.3431i	0.498791	+	0.498791i
$431$	−22.8492	+	22.8492i	−1.10061	+	1.10061i	−0.106272	+	0.994337i	$0.533891\pi$
$431$	−22.8492	+	22.8492i	−1.10061	+	1.10061i	−0.994337	+	0.106272i	$0.966109\pi$
$432$	−54.6274	+	54.6274i	−2.62826	+	2.62826i
$433$			5.48528i			0.263606i	0.991276	+	0.131803i	$0.0420766\pi$
$433$			5.48528i			0.263606i	−0.991276	+	0.131803i	$0.957923\pi$
$434$		−	2.34315i		−	0.112475i
$435$	12.4853	−	12.4853i	0.598623	−	0.598623i
$436$	2.10051	−	2.10051i	0.100596	−	0.100596i
$437$	16.2426	+	16.2426i	0.776991	+	0.776991i
$438$	94.4264			4.51187
$439$	−1.77817	−	1.77817i	−0.0848676	−	0.0848676i	0.663399	−	0.748266i	$-0.269113\pi$
$439$	−1.77817	−	1.77817i	−0.0848676	−	0.0848676i	−0.748266	+	0.663399i	$0.769113\pi$
$440$		0			0
$441$	−51.9411			−2.47339
$442$	4.14214	−	2.48528i	0.197021	−	0.118213i
$443$	−20.9706			−0.996342			−0.498171	−	0.867079i	$-0.665995\pi$
$443$	−20.9706			−0.996342			−0.498171	+	0.867079i	$0.665995\pi$
$444$		−	44.9706i		−	2.13421i
$445$	7.65685	+	7.65685i	0.362970	+	0.362970i
$446$	12.0000			0.568216
$447$	−28.3848	−	28.3848i	−1.34255	−	1.34255i
$448$	−5.65685	+	5.65685i	−0.267261	+	0.267261i
$449$	11.3137	−	11.3137i	0.533927	−	0.533927i	−0.387812	−	0.921739i	$-0.626769\pi$
$449$	11.3137	−	11.3137i	0.533927	−	0.533927i	0.921739	+	0.387812i	$0.126769\pi$
$450$		−	51.9411i		−	2.44853i
$451$			5.00000i			0.235441i
$452$	5.17157	−	5.17157i	0.243250	−	0.243250i
$453$	25.3137	−	25.3137i	1.18934	−	1.18934i
$454$	11.5563	+	11.5563i	0.542366	+	0.542366i
$455$	1.65685			0.0776745
$456$		0			0
$457$			19.5147i			0.912860i	0.889759	+	0.456430i	$0.150872\pi$
$457$			19.5147i			0.912860i	−0.889759	+	0.456430i	$0.849128\pi$
$458$	13.3137			0.622109
$459$	77.2548	+	19.3137i	3.60595	+	0.901487i
$460$	−24.0000			−1.11901
$461$			25.6985i			1.19690i	0.801161	+	0.598449i	$0.204216\pi$
$461$			25.6985i			1.19690i	−0.801161	+	0.598449i	$0.795784\pi$
$462$	−4.82843	−	4.82843i	−0.224639	−	0.224639i
$463$	−22.1127			−1.02766			−0.513832	−	0.857891i	$-0.671775\pi$
$463$	−22.1127			−1.02766			−0.513832	+	0.857891i	$0.671775\pi$
$464$	−5.17157	−	5.17157i	−0.240084	−	0.240084i
$465$	8.00000	−	8.00000i	0.370991	−	0.370991i
$466$	16.9289	−	16.9289i	0.784218	−	0.784218i
$467$		−	34.1127i		−	1.57855i	−0.614042	−	0.789274i	$-0.710457\pi$
$467$		−	34.1127i		−	1.57855i	0.614042	−	0.789274i	$-0.289543\pi$
$468$			10.1421i			0.468820i
$469$	−0.707107	+	0.707107i	−0.0326512	+	0.0326512i
$470$	21.9411	−	21.9411i	1.01207	−	1.01207i
$471$	−5.58579	−	5.58579i	−0.257379	−	0.257379i
$472$		0			0
$473$	1.82843	+	1.82843i	0.0840712	+	0.0840712i
$474$		−	60.2843i		−	2.76895i
$475$	−16.2426			−0.745263
$476$	8.00000	+	2.00000i	0.366679	+	0.0916698i
$477$	116.740			5.34516
$478$			21.8579i			0.999755i
$479$	9.05025	+	9.05025i	0.413517	+	0.413517i	0.882962	−	0.469445i	$-0.155546\pi$
$479$	9.05025	+	9.05025i	0.413517	+	0.413517i	−0.469445	+	0.882962i	$0.655546\pi$
$480$	−77.2548			−3.52618
$481$	2.72792	+	2.72792i	0.124383	+	0.124383i
$482$	34.8701	−	34.8701i	1.58829	−	1.58829i
$483$	10.2426	−	10.2426i	0.466056	−	0.466056i
$484$			2.00000i			0.0909091i
$485$		−	10.3431i		−	0.469658i
$486$	−111.054	+	111.054i	−5.03750	+	5.03750i
$487$	0.171573	−	0.171573i	0.00777471	−	0.00777471i	−0.703209	−	0.710983i	$-0.748250\pi$
$487$	0.171573	−	0.171573i	0.00777471	−	0.00777471i	0.710983	+	0.703209i	$0.248250\pi$
$488$		0			0
$489$	24.1421			1.09175
$490$	−24.0000	−	24.0000i	−1.08421	−	1.08421i
$491$			1.61522i			0.0728940i	0.999336	+	0.0364470i	$0.0116040\pi$
$491$			1.61522i			0.0728940i	−0.999336	+	0.0364470i	$0.988396\pi$
$492$	34.1421			1.53925
$493$	−1.82843	+	7.31371i	−0.0823482	+	0.329393i
$494$	6.34315			0.285392
$495$		−	24.4853i		−	1.10053i
$496$	−3.31371	−	3.31371i	−0.148790	−	0.148790i
$497$	−4.34315			−0.194817
$498$	−4.00000	−	4.00000i	−0.179244	−	0.179244i
$499$	5.07107	−	5.07107i	0.227012	−	0.227012i	−0.584431	−	0.811443i	$-0.698682\pi$
$499$	5.07107	−	5.07107i	0.227012	−	0.227012i	0.811443	+	0.584431i	$0.198682\pi$
$500$	−8.00000	+	8.00000i	−0.357771	+	0.357771i
$501$		−	82.4264i		−	3.68254i
$502$			12.0000i			0.535586i
$503$	−8.02082	+	8.02082i	−0.357630	+	0.357630i	−0.862939	−	0.505308i	$-0.831379\pi$
$503$	−8.02082	+	8.02082i	−0.357630	+	0.357630i	0.505308	+	0.862939i	$0.331379\pi$
$504$		0			0
$505$	29.4558	+	29.4558i	1.31077	+	1.31077i
$506$	−8.48528			−0.377217
$507$	30.5563	+	30.5563i	1.35706	+	1.35706i
$508$		−	28.4853i		−	1.26383i
$509$	17.6863			0.783931			0.391966	−	0.919980i	$-0.371795\pi$
$509$	17.6863			0.783931			0.391966	+	0.919980i	$0.371795\pi$
$510$	40.9706	+	68.2843i	1.81421	+	3.02368i
$511$	−13.8284			−0.611734
$512$			32.0000i			1.41421i
$513$	73.9411	+	73.9411i	3.26458	+	3.26458i
$514$	−54.9706			−2.42465
$515$	10.6863	+	10.6863i	0.470894	+	0.470894i
$516$	12.4853	−	12.4853i	0.549634	−	0.549634i
$517$	3.87868	−	3.87868i	0.170584	−	0.170584i
$518$			13.1716i			0.578726i
$519$			19.8995i			0.873491i
$520$		0			0
$521$	−5.24264	+	5.24264i	−0.229684	+	0.229684i	−0.812561	−	0.582876i	$-0.801927\pi$
$521$	−5.24264	+	5.24264i	−0.229684	+	0.229684i	0.582876	+	0.812561i	$0.301927\pi$
$522$	−22.3848	−	22.3848i	−0.979755	−	0.979755i
$523$	−17.6569			−0.772080			−0.386040	−	0.922482i	$-0.626157\pi$
$523$	−17.6569			−0.772080			−0.386040	+	0.922482i	$0.626157\pi$
$524$	−11.0711	−	11.0711i	−0.483642	−	0.483642i
$525$			10.2426i			0.447025i
$526$	−51.1127			−2.22862
$527$	−1.17157	+	4.68629i	−0.0510345	+	0.204138i
$528$	−13.6569			−0.594338
$529$			5.00000i			0.217391i
$530$	53.9411	+	53.9411i	2.34305	+	2.34305i
$531$	−57.6274			−2.50082
$532$	7.65685	+	7.65685i	0.331967	+	0.331967i
$533$	−2.07107	+	2.07107i	−0.0897079	+	0.0897079i
$534$	18.4853	−	18.4853i	0.799936	−	0.799936i
$535$		−	30.1421i		−	1.30316i
$536$		0			0
$537$	−47.3848	+	47.3848i	−2.04480	+	2.04480i
$538$	−3.85786	+	3.85786i	−0.166324	+	0.166324i
$539$	−4.24264	−	4.24264i	−0.182743	−	0.182743i
$540$	−109.255			−4.70158
$541$	−21.4350	−	21.4350i	−0.921564	−	0.921564i	0.0755762	−	0.997140i	$-0.475920\pi$
$541$	−21.4350	−	21.4350i	−0.921564	−	0.921564i	−0.997140	+	0.0755762i	$0.975920\pi$
$542$		−	13.3726i		−	0.574402i
$543$	−5.17157			−0.221933
$544$	28.2843	−	16.9706i	1.21268	−	0.727607i
$545$	−4.20101			−0.179952
$546$		−	4.00000i		−	0.171184i
$547$	−25.8995	−	25.8995i	−1.10738	−	1.10738i	−0.993493	−	0.113889i	$-0.963669\pi$
$547$	−25.8995	−	25.8995i	−1.10738	−	1.10738i	−0.113889	−	0.993493i	$-0.536331\pi$
$548$	−8.34315			−0.356402
$549$	7.17157	+	7.17157i	0.306075	+	0.306075i
$550$	4.24264	−	4.24264i	0.180907	−	0.180907i
$551$	−7.00000	+	7.00000i	−0.298210	+	0.298210i
$552$		0			0
$553$			8.82843i			0.375423i
$554$	35.0711	−	35.0711i	1.49003	−	1.49003i
$555$	−44.9706	+	44.9706i	−1.90889	+	1.90889i
$556$	16.7279	+	16.7279i	0.709422	+	0.709422i
$557$	−32.2843			−1.36793			−0.683964	−	0.729516i	$-0.739746\pi$
$557$	−32.2843			−1.36793			−0.683964	+	0.729516i	$0.739746\pi$
$558$	−14.3431	−	14.3431i	−0.607194	−	0.607194i
$559$			1.51472i			0.0640658i
$560$	11.3137			0.478091
$561$	7.24264	+	12.0711i	0.305785	+	0.509641i
$562$	0.970563			0.0409407
$563$			36.8701i			1.55389i	0.629570	+	0.776944i	$0.283231\pi$
$563$			36.8701i			1.55389i	−0.629570	+	0.776944i	$0.716769\pi$
$564$	−26.4853	−	26.4853i	−1.11523	−	1.11523i
$565$	−10.3431			−0.435139
$566$	26.1421	+	26.1421i	1.09884	+	1.09884i
$567$	28.2635	−	28.2635i	1.18695	−	1.18695i
$568$		0			0
$569$		−	36.4853i		−	1.52954i	−0.644302	−	0.764771i	$-0.722852\pi$
$569$		−	36.4853i		−	1.52954i	0.644302	−	0.764771i	$-0.277148\pi$
$570$			104.569i			4.37989i
$571$	20.2635	−	20.2635i	0.847999	−	0.847999i	−0.141884	−	0.989883i	$-0.545316\pi$
$571$	20.2635	−	20.2635i	0.847999	−	0.847999i	0.989883	+	0.141884i	$0.0453160\pi$
$572$	−0.828427	+	0.828427i	−0.0346383	+	0.0346383i
$573$	−30.9706	−	30.9706i	−1.29381	−	1.29381i
$574$	−10.0000			−0.417392
$575$	9.00000	+	9.00000i	0.375326	+	0.375326i
$576$			69.2548i			2.88562i
$577$	44.3137			1.84480			0.922402	−	0.386231i	$-0.126223\pi$
$577$	44.3137			1.84480			0.922402	+	0.386231i	$0.126223\pi$
$578$	−30.0000	−	16.0000i	−1.24784	−	0.665512i
$579$	−71.5980			−2.97551
$580$		−	10.3431i		−	0.429476i
$581$	0.585786	+	0.585786i	0.0243025	+	0.0243025i
$582$	−24.9706			−1.03506
$583$	9.53553	+	9.53553i	0.394921	+	0.394921i
$584$		0			0
$585$	10.1421	−	10.1421i	0.419326	−	0.419326i
$586$			50.1421i			2.07135i
$587$		−	25.1127i		−	1.03651i	−0.855226	−	0.518256i	$-0.826581\pi$
$587$		−	25.1127i		−	1.03651i	0.855226	−	0.518256i	$-0.173419\pi$
$588$	−28.9706	+	28.9706i	−1.19473	+	1.19473i
$589$	−4.48528	+	4.48528i	−0.184813	+	0.184813i
$590$	−26.6274	−	26.6274i	−1.09623	−	1.09623i
$591$	−11.3137			−0.465384
$592$	18.6274	+	18.6274i	0.765582	+	0.765582i
$593$			2.68629i			0.110313i	0.998478	+	0.0551564i	$0.0175657\pi$
$593$			2.68629i			0.110313i	−0.998478	+	0.0551564i	$0.982434\pi$
$594$	−38.6274			−1.58490
$595$	−6.00000	−	10.0000i	−0.245976	−	0.409960i
$596$	−23.5147			−0.963200
$597$			60.7696i			2.48713i
$598$	−3.51472	−	3.51472i	−0.143728	−	0.143728i
$599$	27.9706			1.14285			0.571423	−	0.820656i	$-0.306392\pi$
$599$	27.9706			1.14285			0.571423	+	0.820656i	$0.306392\pi$
$600$		0			0
$601$	3.31371	−	3.31371i	0.135169	−	0.135169i	−0.636285	−	0.771454i	$-0.719530\pi$
$601$	3.31371	−	3.31371i	0.135169	−	0.135169i	0.771454	+	0.636285i	$0.219530\pi$
$602$	−3.65685	+	3.65685i	−0.149042	+	0.149042i
$603$			8.65685i			0.352534i
$604$		−	20.9706i		−	0.853280i
$605$	2.00000	−	2.00000i	0.0813116	−	0.0813116i
$606$	71.1127	−	71.1127i	2.88876	−	2.88876i
$607$	7.27208	+	7.27208i	0.295165	+	0.295165i	0.839116	−	0.543952i	$-0.183073\pi$
$607$	7.27208	+	7.27208i	0.295165	+	0.295165i	−0.543952	+	0.839116i	$0.683073\pi$
$608$	43.3137			1.75660
$609$	4.41421	+	4.41421i	0.178873	+	0.178873i
$610$			6.62742i			0.268336i
$611$	3.21320			0.129992
$612$	61.2132	−	36.7279i	2.47440	−	1.48464i
$613$	36.7279			1.48343			0.741713	−	0.670717i	$-0.234013\pi$
$613$	36.7279			1.48343			0.741713	+	0.670717i	$0.234013\pi$
$614$		−	27.5147i		−	1.11040i
$615$	−34.1421	−	34.1421i	−1.37674	−	1.37674i
$616$		0			0
$617$	−16.9706	−	16.9706i	−0.683209	−	0.683209i	0.277513	−	0.960722i	$-0.410490\pi$
$617$	−16.9706	−	16.9706i	−0.683209	−	0.683209i	−0.960722	+	0.277513i	$0.910490\pi$
$618$	25.7990	−	25.7990i	1.03779	−	1.03779i
$619$	−6.92893	+	6.92893i	−0.278497	+	0.278497i	−0.832509	−	0.554012i	$-0.813096\pi$
$619$	−6.92893	+	6.92893i	−0.278497	+	0.278497i	0.554012	+	0.832509i	$0.313096\pi$
$620$		−	6.62742i		−	0.266163i
$621$		−	81.9411i		−	3.28818i
$622$	19.3137	−	19.3137i	0.774409	−	0.774409i
$623$	−2.70711	+	2.70711i	−0.108458	+	0.108458i
$624$	−5.65685	−	5.65685i	−0.226455	−	0.226455i
$625$	31.0000			1.24000
$626$	−15.1716	−	15.1716i	−0.606378	−	0.606378i
$627$			18.4853i			0.738231i
$628$	−4.62742			−0.184654
$629$	6.58579	−	26.3431i	0.262593	−	1.05037i
$630$	48.9706			1.95103
$631$		−	20.6569i		−	0.822336i	−0.911559	−	0.411168i	$-0.865121\pi$
$631$		−	20.6569i		−	0.822336i	0.911559	−	0.411168i	$-0.134879\pi$
$632$		0			0
$633$	30.7279			1.22133
$634$	22.8284	+	22.8284i	0.906633	+	0.906633i
$635$	−28.4853	+	28.4853i	−1.13040	+	1.13040i
$636$	65.1127	−	65.1127i	2.58189	−	2.58189i
$637$		−	3.51472i		−	0.139258i
$638$		−	3.65685i		−	0.144776i
$639$	−26.5858	+	26.5858i	−1.05172	+	1.05172i
$640$		0			0
$641$	1.58579	+	1.58579i	0.0626348	+	0.0626348i	0.737730	−	0.675096i	$-0.235898\pi$
$641$	1.58579	+	1.58579i	0.0626348	+	0.0626348i	−0.675096	+	0.737730i	$0.735898\pi$
$642$	−72.7696			−2.87199
$643$	−19.7279	−	19.7279i	−0.777993	−	0.777993i	0.201496	−	0.979489i	$-0.435420\pi$
$643$	−19.7279	−	19.7279i	−0.777993	−	0.777993i	−0.979489	+	0.201496i	$0.935420\pi$
$644$		−	8.48528i		−	0.334367i
$645$	−24.9706			−0.983215
$646$	−22.9706	−	38.2843i	−0.903765	−	1.50627i
$647$	22.4558			0.882830			0.441415	−	0.897303i	$-0.354477\pi$
$647$	22.4558			0.882830			0.441415	+	0.897303i	$0.354477\pi$
$648$		0			0
$649$	−4.70711	−	4.70711i	−0.184770	−	0.184770i
$650$	3.51472			0.137859
$651$	2.82843	+	2.82843i	0.110855	+	0.110855i
$652$	10.0000	−	10.0000i	0.391630	−	0.391630i
$653$	−17.8995	+	17.8995i	−0.700461	+	0.700461i	−0.964510	−	0.264048i	$-0.914942\pi$
$653$	−17.8995	+	17.8995i	−0.700461	+	0.700461i	0.264048	+	0.964510i	$0.414942\pi$
$654$			10.1421i			0.396589i
$655$			22.1421i			0.865165i
$656$	−14.1421	+	14.1421i	−0.552158	+	0.552158i
$657$	−84.6482	+	84.6482i	−3.30244	+	3.30244i
$658$	7.75736	+	7.75736i	0.302413	+	0.302413i
$659$	−22.5269			−0.877524			−0.438762	−	0.898603i	$-0.644583\pi$
$659$	−22.5269			−0.877524			−0.438762	+	0.898603i	$0.644583\pi$
$660$	−13.6569	−	13.6569i	−0.531592	−	0.531592i
$661$		−	21.0000i		−	0.816805i	−0.912802	−	0.408403i	$-0.866086\pi$
$661$		−	21.0000i		−	0.816805i	0.912802	−	0.408403i	$-0.133914\pi$
$662$	0.686292			0.0266735
$663$	−2.00000	+	8.00000i	−0.0776736	+	0.310694i
$664$		0			0
$665$		−	15.3137i		−	0.593840i
$666$	80.6274	+	80.6274i	3.12425	+	3.12425i
$667$	7.75736			0.300366
$668$	−34.1421	−	34.1421i	−1.32100	−	1.32100i
$669$	−14.4853	+	14.4853i	−0.560033	+	0.560033i
$670$	−4.00000	+	4.00000i	−0.154533	+	0.154533i
$671$			1.17157i			0.0452281i
$672$		−	27.3137i		−	1.05365i
$673$	11.0503	−	11.0503i	0.425956	−	0.425956i	−0.461292	−	0.887248i	$-0.652614\pi$
$673$	11.0503	−	11.0503i	0.425956	−	0.425956i	0.887248	+	0.461292i	$0.152614\pi$
$674$	20.5269	−	20.5269i	0.790667	−	0.790667i
$675$	40.9706	+	40.9706i	1.57696	+	1.57696i
$676$	25.3137			0.973604
$677$	15.9203	+	15.9203i	0.611867	+	0.611867i	0.943432	−	0.331565i	$-0.107577\pi$
$677$	15.9203	+	15.9203i	0.611867	+	0.611867i	−0.331565	+	0.943432i	$0.607577\pi$
$678$			24.9706i			0.958989i
$679$	3.65685			0.140337
$680$		0			0
$681$	−27.8995			−1.06911
$682$		−	2.34315i		−	0.0897237i
$683$	6.21320	+	6.21320i	0.237742	+	0.237742i	0.815914	−	0.578173i	$-0.196234\pi$
$683$	6.21320	+	6.21320i	0.237742	+	0.237742i	−0.578173	+	0.815914i	$0.696234\pi$
$684$	93.7401			3.58424
$685$	8.34315	+	8.34315i	0.318775	+	0.318775i
$686$	18.3848	−	18.3848i	0.701934	−	0.701934i
$687$	−16.0711	+	16.0711i	−0.613149	+	0.613149i
$688$			10.3431i			0.394329i
$689$			7.89949i			0.300947i
$690$	57.9411	−	57.9411i	2.20578	−	2.20578i
$691$	18.7574	−	18.7574i	0.713564	−	0.713564i	−0.253715	−	0.967279i	$-0.581653\pi$
$691$	18.7574	−	18.7574i	0.713564	−	0.713564i	0.967279	+	0.253715i	$0.0816526\pi$
$692$	8.24264	+	8.24264i	0.313338	+	0.313338i
$693$	8.65685			0.328847
$694$	−22.8701	−	22.8701i	−0.868136	−	0.868136i
$695$		−	33.4558i		−	1.26905i
$696$		0			0
$697$	20.0000	+	5.00000i	0.757554	+	0.189389i
$698$	−47.3970			−1.79400
$699$			40.8701i			1.54585i
$700$	4.24264	+	4.24264i	0.160357	+	0.160357i
$701$	−38.1421			−1.44061			−0.720304	−	0.693658i	$-0.755998\pi$
$701$	−38.1421			−1.44061			−0.720304	+	0.693658i	$0.755998\pi$
$702$	−16.0000	−	16.0000i	−0.603881	−	0.603881i
$703$	25.2132	−	25.2132i	0.950934	−	0.950934i
$704$	−5.65685	+	5.65685i	−0.213201	+	0.213201i
$705$			52.9706i			1.99499i
$706$		−	35.6569i		−	1.34196i
$707$	−10.4142	+	10.4142i	−0.391667	+	0.391667i
$708$	−32.1421	+	32.1421i	−1.20798	+	1.20798i
$709$	−2.07107	−	2.07107i	−0.0777806	−	0.0777806i	0.667146	−	0.744927i	$-0.267516\pi$
$709$	−2.07107	−	2.07107i	−0.0777806	−	0.0777806i	−0.744927	+	0.667146i	$0.767516\pi$
$710$	−24.5685			−0.922041
$711$	54.0416	+	54.0416i	2.02672	+	2.02672i
$712$		0			0
$713$	4.97056			0.186149
$714$	−24.1421	+	14.4853i	−0.903497	+	0.542098i
$715$	1.65685			0.0619628
$716$			39.2548i			1.46702i
$717$	−26.3848	−	26.3848i	−0.985358	−	0.985358i
$718$	7.71573			0.287948
$719$	14.5563	+	14.5563i	0.542860	+	0.542860i	0.924366	−	0.381506i	$-0.124594\pi$
$719$	14.5563	+	14.5563i	0.542860	+	0.542860i	−0.381506	+	0.924366i	$0.624594\pi$
$720$	69.2548	−	69.2548i	2.58098	−	2.58098i
$721$	−3.77817	+	3.77817i	−0.140707	+	0.140707i
$722$		−	20.6274i		−	0.767673i
$723$			84.1838i			3.13083i
$724$	−2.14214	+	2.14214i	−0.0796118	+	0.0796118i
$725$	−3.87868	+	3.87868i	−0.144051	+	0.144051i
$726$	−4.82843	−	4.82843i	−0.179200	−	0.179200i
$727$	23.1421			0.858294			0.429147	−	0.903235i	$-0.358814\pi$
$727$	23.1421			0.858294			0.429147	+	0.903235i	$0.358814\pi$
$728$		0			0
$729$		−	148.196i		−	5.48874i
$730$	−78.2254			−2.89525
$731$	9.14214	−	5.48528i	0.338134	−	0.202880i
$732$	8.00000			0.295689
$733$			5.79899i			0.214191i	0.994249	+	0.107095i	$0.0341550\pi$
$733$			5.79899i			0.214191i	−0.994249	+	0.107095i	$0.965845\pi$
$734$	−14.3431	−	14.3431i	−0.529415	−	0.529415i
$735$	57.9411			2.13719
$736$	−24.0000	−	24.0000i	−0.884652	−	0.884652i
$737$	−0.707107	+	0.707107i	−0.0260466	+	0.0260466i
$738$	−61.2132	+	61.2132i	−2.25329	+	2.25329i
$739$		−	12.6863i		−	0.466673i	−0.972396	−	0.233336i	$-0.925036\pi$
$739$		−	12.6863i		−	0.466673i	0.972396	−	0.233336i	$-0.0749643\pi$
$740$			37.2548i			1.36951i
$741$	−7.65685	+	7.65685i	−0.281282	+	0.281282i
$742$	−19.0711	+	19.0711i	−0.700121	+	0.700121i
$743$	21.4350	+	21.4350i	0.786375	+	0.786375i	0.980898	−	0.194523i	$-0.0623159\pi$
$743$	21.4350	+	21.4350i	0.786375	+	0.786375i	−0.194523	+	0.980898i	$0.562316\pi$
$744$		0			0
$745$	23.5147	+	23.5147i	0.861513	+	0.861513i
$746$			6.54416i			0.239599i
$747$	7.17157			0.262394
$748$	8.00000	+	2.00000i	0.292509	+	0.0731272i
$749$	10.6569			0.389393
$750$		−	38.6274i		−	1.41047i
$751$	17.3848	+	17.3848i	0.634379	+	0.634379i	0.949163	−	0.314784i	$-0.101932\pi$
$751$	17.3848	+	17.3848i	0.634379	+	0.634379i	−0.314784	+	0.949163i	$0.601932\pi$
$752$	21.9411			0.800111
$753$	−14.4853	−	14.4853i	−0.527873	−	0.527873i
$754$	1.51472	−	1.51472i	0.0551628	−	0.0551628i
$755$	−20.9706	+	20.9706i	−0.763197	+	0.763197i
$756$		−	38.6274i		−	1.40487i
$757$		−	22.8284i		−	0.829713i	−0.909887	−	0.414857i	$-0.863832\pi$
$757$		−	22.8284i		−	0.829713i	0.909887	−	0.414857i	$-0.136168\pi$
$758$	−13.1127	+	13.1127i	−0.476275	+	0.476275i
$759$	10.2426	−	10.2426i	0.371784	−	0.371784i
$760$		0			0
$761$	19.0711			0.691326			0.345663	−	0.938359i	$-0.387654\pi$
$761$	19.0711			0.691326			0.345663	+	0.938359i	$0.387654\pi$
$762$	68.7696	+	68.7696i	2.49126	+	2.49126i
$763$		−	1.48528i		−	0.0537708i
$764$	−25.6569			−0.928232
$765$	−97.9411	−	24.4853i	−3.54107	−	0.885267i
$766$	38.9117			1.40594
$767$		−	3.89949i		−	0.140803i
$768$	−38.6274	−	38.6274i	−1.39385	−	1.39385i
$769$	34.0416			1.22757			0.613786	−	0.789472i	$-0.289646\pi$
$769$	34.0416			1.22757			0.613786	+	0.789472i	$0.289646\pi$
$770$	4.00000	+	4.00000i	0.144150	+	0.144150i
$771$	66.3553	−	66.3553i	2.38973	−	2.38973i
$772$	−29.6569	+	29.6569i	−1.06737	+	1.06737i
$773$		−	37.5980i		−	1.35231i	−0.736762	−	0.676153i	$-0.763646\pi$
$773$		−	37.5980i		−	1.35231i	0.736762	−	0.676153i	$-0.236354\pi$
$774$			44.7696i			1.60921i
$775$	−2.48528	+	2.48528i	−0.0892739	+	0.0892739i
$776$		0			0
$777$	−15.8995	−	15.8995i	−0.570391	−	0.570391i
$778$	18.0000			0.645331
$779$	19.1421	+	19.1421i	0.685838	+	0.685838i
$780$		−	11.3137i		−	0.405096i
$781$	−4.34315			−0.155410
$782$	−8.48528	+	33.9411i	−0.303433	+	1.21373i
$783$	35.3137			1.26201
$784$		−	24.0000i		−	0.857143i
$785$	4.62742	+	4.62742i	0.165160	+	0.165160i
$786$	53.4558			1.90671
$787$	4.36396	+	4.36396i	0.155558	+	0.155558i	0.780595	−	0.625037i	$-0.214916\pi$
$787$	4.36396	+	4.36396i	0.155558	+	0.155558i	−0.625037	+	0.780595i	$0.714916\pi$
$788$	−4.68629	+	4.68629i	−0.166942	+	0.166942i
$789$	61.6985	−	61.6985i	2.19652	−	2.19652i
$790$			49.9411i			1.77683i
$791$		−	3.65685i		−	0.130023i
$792$		0			0
$793$	−0.485281	+	0.485281i	−0.0172328	+	0.0172328i
$794$	−51.4558	−	51.4558i	−1.82610	−	1.82610i
$795$	−130.225			−4.61862
$796$	25.1716	+	25.1716i	0.892183	+	0.892183i
$797$			36.4853i			1.29237i	0.763179	+	0.646187i	$0.223638\pi$
$797$			36.4853i			1.29237i	−0.763179	+	0.646187i	$0.776362\pi$
$798$	−36.9706			−1.30874
$799$	−11.6360	−	19.3934i	−0.411653	−	0.686089i
$800$	24.0000			0.848528
$801$			33.1421i			1.17102i
$802$	16.9706	+	16.9706i	0.599251	+	0.599251i
$803$	−13.8284			−0.487995
$804$	4.82843	+	4.82843i	0.170285	+	0.170285i
$805$	−8.48528	+	8.48528i	−0.299067	+	0.299067i
$806$	0.970563	−	0.970563i	0.0341866	−	0.0341866i
$807$		−	9.31371i		−	0.327858i
$808$		0			0
$809$	−11.3934	+	11.3934i	−0.400571	+	0.400571i	−0.878434	−	0.477864i	$-0.841411\pi$
$809$	−11.3934	+	11.3934i	−0.400571	+	0.400571i	0.477864	+	0.878434i	$0.341411\pi$
$810$	159.882	−	159.882i	5.61769	−	5.61769i
$811$	−8.92893	−	8.92893i	−0.313537	−	0.313537i	0.532741	−	0.846278i	$-0.321162\pi$
$811$	−8.92893	−	8.92893i	−0.313537	−	0.313537i	−0.846278	+	0.532741i	$0.821162\pi$
$812$	3.65685			0.128330
$813$	16.1421	+	16.1421i	0.566129	+	0.566129i
$814$			13.1716i			0.461663i
$815$	−20.0000			−0.700569
$816$	−13.6569	+	54.6274i	−0.478086	+	1.91234i
$817$	14.0000			0.489798
$818$		−	36.2843i		−	1.26865i
$819$	3.58579	+	3.58579i	0.125298	+	0.125298i
$820$	−28.2843			−0.987730
$821$	−22.8284	−	22.8284i	−0.796718	−	0.796718i	0.185859	−	0.982576i	$-0.440493\pi$
$821$	−22.8284	−	22.8284i	−0.796718	−	0.796718i	−0.982576	+	0.185859i	$0.940493\pi$
$822$	20.1421	−	20.1421i	0.702538	−	0.702538i
$823$	−24.6274	+	24.6274i	−0.858458	+	0.858458i	−0.991156	−	0.132699i	$-0.957636\pi$
$823$	−24.6274	+	24.6274i	−0.858458	+	0.858458i	0.132699	+	0.991156i	$0.457636\pi$
$824$		0			0
$825$			10.2426i			0.356603i
$826$	9.41421	−	9.41421i	0.327562	−	0.327562i
$827$	−34.7487	+	34.7487i	−1.20833	+	1.20833i	−0.236765	+	0.971567i	$0.576087\pi$
$827$	−34.7487	+	34.7487i	−1.20833	+	1.20833i	−0.971567	+	0.236765i	$0.923913\pi$
$828$	−51.9411	−	51.9411i	−1.80508	−	1.80508i
$829$	−0.970563			−0.0337090			−0.0168545	−	0.999858i	$-0.505365\pi$
$829$	−0.970563			−0.0337090			−0.0168545	+	0.999858i	$0.505365\pi$
$830$	3.31371	+	3.31371i	0.115021	+	0.115021i
$831$			84.6690i			2.93714i
$832$	−4.68629			−0.162468
$833$	−21.2132	+	12.7279i	−0.734994	+	0.440996i
$834$	−80.7696			−2.79682
$835$			68.2843i			2.36307i
$836$	7.65685	+	7.65685i	0.264818	+	0.264818i
$837$	22.6274			0.782118
$838$	39.3137	+	39.3137i	1.35807	+	1.35807i
$839$	11.3848	−	11.3848i	0.393046	−	0.393046i	−0.482726	−	0.875772i	$-0.660353\pi$
$839$	11.3848	−	11.3848i	0.393046	−	0.393046i	0.875772	+	0.482726i	$0.160353\pi$
$840$		0			0
$841$		−	25.6569i		−	0.884719i
$842$			4.62742i			0.159471i
$843$	−1.17157	+	1.17157i	−0.0403511	+	0.0403511i
$844$	12.7279	−	12.7279i	0.438113	−	0.438113i
$845$	−25.3137	−	25.3137i	−0.870818	−	0.870818i
$846$	94.9706			3.26516
$847$	0.707107	+	0.707107i	0.0242965	+	0.0242965i
$848$			53.9411i			1.85235i
$849$	−63.1127			−2.16602
$850$	−12.7279	−	21.2132i	−0.436564	−	0.727607i
$851$	−27.9411			−0.957809
$852$			29.6569i			1.01603i
$853$	−27.9203	−	27.9203i	−0.955973	−	0.955973i	0.0430977	−	0.999071i	$-0.486277\pi$
$853$	−27.9203	−	27.9203i	−0.955973	−	0.955973i	−0.999071	+	0.0430977i	$0.986277\pi$
$854$	−2.34315			−0.0801808
$855$	−93.7401	−	93.7401i	−3.20584	−	3.20584i
$856$		0			0
$857$	−11.4558	+	11.4558i	−0.391324	+	0.391324i	−0.875159	−	0.483835i	$-0.839243\pi$
$857$	−11.4558	+	11.4558i	−0.391324	+	0.391324i	0.483835	+	0.875159i	$0.339243\pi$
$858$		−	4.00000i		−	0.136558i
$859$			12.3137i			0.420138i	0.977687	+	0.210069i	$0.0673689\pi$
$859$			12.3137i			0.420138i	−0.977687	+	0.210069i	$0.932631\pi$
$860$	−10.3431	+	10.3431i	−0.352698	+	0.352698i
$861$	12.0711	−	12.0711i	0.411381	−	0.411381i
$862$	−45.6985	−	45.6985i	−1.55650	−	1.55650i
$863$	−53.3137			−1.81482			−0.907410	−	0.420247i	$-0.861944\pi$
$863$	−53.3137			−1.81482			−0.907410	+	0.420247i	$0.861944\pi$
$864$	−109.255	−	109.255i	−3.71692	−	3.71692i
$865$		−	16.4853i		−	0.560516i
$866$	−10.9706			−0.372795
$867$	55.5269	−	16.8995i	1.88579	−	0.573937i
$868$	2.34315			0.0795315
$869$			8.82843i			0.299484i
$870$	24.9706	+	24.9706i	0.846581	+	0.846581i
$871$	−0.585786			−0.0198486
$872$		0			0
$873$	22.3848	−	22.3848i	0.757610	−	0.757610i
$874$	−32.4853	+	32.4853i	−1.09883	+	1.09883i
$875$			5.65685i			0.191237i
$876$			94.4264i			3.19037i
$877$	19.5563	−	19.5563i	0.660371	−	0.660371i	−0.295096	−	0.955467i	$-0.595352\pi$
$877$	19.5563	−	19.5563i	0.660371	−	0.660371i	0.955467	+	0.295096i	$0.0953518\pi$
$878$	3.55635	−	3.55635i	0.120021	−	0.120021i
$879$	−60.5269	−	60.5269i	−2.04152	−	2.04152i
$880$	11.3137			0.381385
$881$	−12.5858	−	12.5858i	−0.424026	−	0.424026i	0.462561	−	0.886587i	$-0.346930\pi$
$881$	−12.5858	−	12.5858i	−0.424026	−	0.424026i	−0.886587	+	0.462561i	$0.846930\pi$
$882$		−	103.882i		−	3.49790i
$883$	9.34315			0.314422			0.157211	−	0.987565i	$-0.449750\pi$
$883$	9.34315			0.314422			0.157211	+	0.987565i	$0.449750\pi$
$884$	2.48528	+	4.14214i	0.0835891	+	0.139315i
$885$	64.2843			2.16089
$886$		−	41.9411i		−	1.40904i
$887$	−20.4853	−	20.4853i	−0.687828	−	0.687828i	0.273923	−	0.961752i	$-0.411679\pi$
$887$	−20.4853	−	20.4853i	−0.687828	−	0.687828i	−0.961752	+	0.273923i	$0.911679\pi$
$888$		0			0
$889$	−10.0711	−	10.0711i	−0.337773	−	0.337773i
$890$	−15.3137	+	15.3137i	−0.513317	+	0.513317i
$891$	28.2635	−	28.2635i	0.946861	−	0.946861i
$892$			12.0000i			0.401790i
$893$		−	29.6985i		−	0.993822i
$894$	56.7696	−	56.7696i	1.89866	−	1.89866i
$895$	39.2548	−	39.2548i	1.31214	−	1.31214i
$896$		0			0
$897$	8.48528			0.283315
$898$	22.6274	+	22.6274i	0.755087	+	0.755087i
$899$			2.14214i			0.0714442i
$900$	51.9411			1.73137
$901$	47.6777	−	28.6066i	1.58837	−	0.953024i
$902$	−10.0000			−0.332964
$903$		−	8.82843i		−	0.293792i
$904$		0			0
$905$	4.28427			0.142414
$906$	50.6274	+	50.6274i	1.68198	+	1.68198i
$907$	−14.7279	+	14.7279i	−0.489033	+	0.489033i	−0.908001	−	0.418968i	$-0.862392\pi$
$907$	−14.7279	+	14.7279i	−0.489033	+	0.489033i	0.418968	+	0.908001i	$0.362392\pi$
$908$	−11.5563	+	11.5563i	−0.383511	+	0.383511i
$909$			127.497i			4.22882i
$910$			3.31371i			0.109848i
$911$	−3.24264	+	3.24264i	−0.107433	+	0.107433i	−0.758780	−	0.651347i	$-0.774204\pi$
$911$	−3.24264	+	3.24264i	−0.107433	+	0.107433i	0.651347	+	0.758780i	$0.274204\pi$
$912$	−52.2843	+	52.2843i	−1.73131	+	1.73131i
$913$	0.585786	+	0.585786i	0.0193867	+	0.0193867i
$914$	−39.0294			−1.29098
$915$	−8.00000	−	8.00000i	−0.264472	−	0.264472i
$916$			13.3137i			0.439897i
$917$	−7.82843			−0.258517
$918$	−38.6274	+	154.510i	−1.27489	+	5.09958i
$919$	−30.0416			−0.990982			−0.495491	−	0.868613i	$-0.665012\pi$
$919$	−30.0416			−0.990982			−0.495491	+	0.868613i	$0.665012\pi$
$920$		0			0
$921$	33.2132	+	33.2132i	1.09441	+	1.09441i
$922$	−51.3970			−1.69267
$923$	−1.79899	−	1.79899i	−0.0592145	−	0.0592145i
$924$	4.82843	−	4.82843i	0.158844	−	0.158844i
$925$	13.9706	−	13.9706i	0.459349	−	0.459349i
$926$		−	44.2254i		−	1.45334i
$927$			46.2548i			1.51921i
$928$	10.3431	−	10.3431i	0.339530	−	0.339530i
$929$	−23.8284	+	23.8284i	−0.781785	+	0.781785i	−0.980132	−	0.198347i	$-0.936443\pi$
$929$	−23.8284	+	23.8284i	−0.781785	+	0.781785i	0.198347	+	0.980132i	$0.436443\pi$
$930$	16.0000	+	16.0000i	0.524661	+	0.524661i
$931$	−32.4853			−1.06466
$932$	16.9289	+	16.9289i	0.554526	+	0.554526i
$933$			46.6274i			1.52651i
$934$	68.2254			2.23240
$935$	−6.00000	−	10.0000i	−0.196221	−	0.327035i
$936$		0			0
$937$			41.3137i			1.34966i	0.737973	+	0.674830i	$0.235783\pi$
$937$			41.3137i			1.34966i	−0.737973	+	0.674830i	$0.764217\pi$
$938$	−1.41421	−	1.41421i	−0.0461757	−	0.0461757i
$939$	36.6274			1.19529
$940$	21.9411	+	21.9411i	0.715641	+	0.715641i
$941$	−12.9497	+	12.9497i	−0.422150	+	0.422150i	−0.885943	−	0.463794i	$-0.846488\pi$
$941$	−12.9497	+	12.9497i	−0.422150	+	0.422150i	0.463794	+	0.885943i	$0.346488\pi$
$942$	11.1716	−	11.1716i	0.363990	−	0.363990i
$943$		−	21.2132i		−	0.690797i
$944$		−	26.6274i		−	0.866649i
$945$	−38.6274	+	38.6274i	−1.25655	+	1.25655i
$946$	−3.65685	+	3.65685i	−0.118895	+	0.118895i
$947$	27.8995	+	27.8995i	0.906612	+	0.906612i	0.995997	−	0.0893854i	$-0.0284903\pi$
$947$	27.8995	+	27.8995i	0.906612	+	0.906612i	−0.0893854	+	0.995997i	$0.528490\pi$
$948$	60.2843			1.95794
$949$	−5.72792	−	5.72792i	−0.185936	−	0.185936i
$950$		−	32.4853i		−	1.05396i
$951$	−55.1127			−1.78715
$952$		0			0
$953$	−30.3431			−0.982911			−0.491455	−	0.870903i	$-0.663535\pi$
$953$	−30.3431			−0.982911			−0.491455	+	0.870903i	$0.663535\pi$
$954$			233.480i			7.55920i
$955$	25.6569	+	25.6569i	0.830236	+	0.830236i
$956$	−21.8579			−0.706934
$957$	4.41421	+	4.41421i	0.142691	+	0.142691i
$958$	−18.1005	+	18.1005i	−0.584801	+	0.584801i
$959$	−2.94975	+	2.94975i	−0.0952523	+	0.0952523i
$960$		−	77.2548i		−	2.49339i
$961$		−	29.6274i		−	0.955723i
$962$	−5.45584	+	5.45584i	−0.175903	+	0.175903i
$963$	65.2340	−	65.2340i	2.10214	−	2.10214i
$964$	34.8701	+	34.8701i	1.12309	+	1.12309i
$965$	59.3137			1.90938
$966$	20.4853	+	20.4853i	0.659103	+	0.659103i
$967$			19.2132i			0.617855i	0.951086	+	0.308927i	$0.0999700\pi$
$967$			19.2132i			0.617855i	−0.951086	+	0.308927i	$0.900030\pi$
$968$		0			0
$969$	73.9411	+	18.4853i	2.37533	+	0.593833i
$970$	20.6863			0.664197
$971$		−	28.4264i		−	0.912247i	−0.889917	−	0.456123i	$-0.849238\pi$
$971$		−	28.4264i		−	0.912247i	0.889917	−	0.456123i	$-0.150762\pi$
$972$	−111.054	−	111.054i	−3.56205	−	3.56205i
$973$	11.8284			0.379202
$974$	0.343146	+	0.343146i	0.0109951	+	0.0109951i
$975$	−4.24264	+	4.24264i	−0.135873	+	0.135873i
$976$	−3.31371	+	3.31371i	−0.106069	+	0.106069i
$977$		−	59.1421i		−	1.89212i	−0.323985	−	0.946062i	$-0.605023\pi$
$977$		−	59.1421i		−	1.89212i	0.323985	−	0.946062i	$-0.394977\pi$
$978$			48.2843i			1.54396i
$979$	−2.70711	+	2.70711i	−0.0865195	+	0.0865195i
$980$	24.0000	−	24.0000i	0.766652	−	0.766652i
$981$	−9.09188	−	9.09188i	−0.290281	−	0.290281i
$982$	−3.23045			−0.103088
$983$	18.2426	+	18.2426i	0.581850	+	0.581850i	0.935411	−	0.353561i	$-0.115029\pi$
$983$	18.2426	+	18.2426i	0.581850	+	0.581850i	−0.353561	+	0.935411i	$0.615029\pi$
$984$		0			0
$985$	9.37258			0.298635
$986$	−14.6274	−	3.65685i	−0.465832	−	0.116458i
$987$	−18.7279			−0.596116
$988$			6.34315i			0.201802i
$989$	−7.75736	−	7.75736i	−0.246670	−	0.246670i
$990$	48.9706			1.55639
$991$	−12.4558	−	12.4558i	−0.395673	−	0.395673i	0.481031	−	0.876704i	$-0.340263\pi$
$991$	−12.4558	−	12.4558i	−0.395673	−	0.395673i	−0.876704	+	0.481031i	$0.840263\pi$
$992$	6.62742	−	6.62742i	0.210421	−	0.210421i
$993$	−0.828427	+	0.828427i	−0.0262893	+	0.0262893i
$994$		−	8.68629i		−	0.275512i
$995$		−	50.3431i		−	1.59599i
$996$	4.00000	−	4.00000i	0.126745	−	0.126745i
$997$	−15.5355	+	15.5355i	−0.492015	+	0.492015i	−0.908941	−	0.416925i	$-0.863108\pi$
$997$	−15.5355	+	15.5355i	−0.492015	+	0.492015i	0.416925	+	0.908941i	$0.363108\pi$
$998$	10.1421	+	10.1421i	0.321044	+	0.321044i
$999$	−127.196			−4.02430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.a.166.1	yes	4
17.2	even	8		3179.2.a.h.1.1		2
17.4	even	4	inner	187.2.e.a.89.1	✓	4
17.15	even	8		3179.2.a.i.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.a.89.1	✓	4	17.4	even	4	inner
187.2.e.a.166.1	yes	4	1.1	even	1	trivial
3179.2.a.h.1.1		2	17.2	even	8
3179.2.a.i.1.2		2	17.15	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +(-2.41421 - 2.41421i) q^{3} -2.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(4.82843 - 4.82843i) q^{6} +(-0.707107 + 0.707107i) q^{7} +8.65685i q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +(-2.41421 - 2.41421i) q^{3} -2.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(4.82843 - 4.82843i) q^{6} +(-0.707107 + 0.707107i) q^{7} +8.65685i q^{9} +(-4.00000 + 4.00000i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(4.82843 + 4.82843i) q^{12} -0.585786 q^{13} +(-1.41421 - 1.41421i) q^{14} -9.65685i q^{15} -4.00000 q^{16} +(2.12132 + 3.53553i) q^{17} -17.3137 q^{18} +5.41421i q^{19} +(-4.00000 - 4.00000i) q^{20} +3.41421 q^{21} +(-1.41421 - 1.41421i) q^{22} +(3.00000 - 3.00000i) q^{23} +3.00000i q^{25} -1.17157i q^{26} +(13.6569 - 13.6569i) q^{27} +(1.41421 - 1.41421i) q^{28} +(1.29289 + 1.29289i) q^{29} +19.3137 q^{30} +(0.828427 + 0.828427i) q^{31} -8.00000i q^{32} +3.41421 q^{33} +(-7.07107 + 4.24264i) q^{34} -2.82843 q^{35} -17.3137i q^{36} +(-4.65685 - 4.65685i) q^{37} -10.8284 q^{38} +(1.41421 + 1.41421i) q^{39} +(3.53553 - 3.53553i) q^{41} +6.82843i q^{42} -2.58579i q^{43} +(1.41421 - 1.41421i) q^{44} +(-17.3137 + 17.3137i) q^{45} +(6.00000 + 6.00000i) q^{46} -5.48528 q^{47} +(9.65685 + 9.65685i) q^{48} +6.00000i q^{49} -6.00000 q^{50} +(3.41421 - 13.6569i) q^{51} +1.17157 q^{52} -13.4853i q^{53} +(27.3137 + 27.3137i) q^{54} -2.82843 q^{55} +(13.0711 - 13.0711i) q^{57} +(-2.58579 + 2.58579i) q^{58} +6.65685i q^{59} +19.3137i q^{60} +(0.828427 - 0.828427i) q^{61} +(-1.65685 + 1.65685i) q^{62} +(-6.12132 - 6.12132i) q^{63} +8.00000 q^{64} +(-1.17157 - 1.17157i) q^{65} +6.82843i q^{66} +1.00000 q^{67} +(-4.24264 - 7.07107i) q^{68} -14.4853 q^{69} -5.65685i q^{70} +(3.07107 + 3.07107i) q^{71} +(9.77817 + 9.77817i) q^{73} +(9.31371 - 9.31371i) q^{74} +(7.24264 - 7.24264i) q^{75} -10.8284i q^{76} -1.00000i q^{77} +(-2.82843 + 2.82843i) q^{78} +(6.24264 - 6.24264i) q^{79} +(-8.00000 - 8.00000i) q^{80} -39.9706 q^{81} +(7.07107 + 7.07107i) q^{82} -0.828427i q^{83} -6.82843 q^{84} +(-2.82843 + 11.3137i) q^{85} +5.17157 q^{86} -6.24264i q^{87} +3.82843 q^{89} +(-34.6274 - 34.6274i) q^{90} +(0.414214 - 0.414214i) q^{91} +(-6.00000 + 6.00000i) q^{92} -4.00000i q^{93} -10.9706i q^{94} +(-10.8284 + 10.8284i) q^{95} +(-19.3137 + 19.3137i) q^{96} +(-2.58579 - 2.58579i) q^{97} -12.0000 q^{98} +(-6.12132 - 6.12132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) 4 * q - 4 * q^3 - 8 * q^4 + 8 * q^5 + 8 * q^6	\( 4 q - 4 q^{3} - 8 q^{4} + 8 q^{5} + 8 q^{6} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 16 q^{16} - 24 q^{18} - 16 q^{20} + 8 q^{21} + 12 q^{23} + 32 q^{27} + 8 q^{29} + 32 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{37} - 32 q^{38} - 24 q^{45} + 24 q^{46} + 12 q^{47} + 16 q^{48} - 24 q^{50} + 8 q^{51} + 16 q^{52} + 64 q^{54} + 24 q^{57} - 16 q^{58} - 8 q^{61} + 16 q^{62} - 16 q^{63} + 32 q^{64} - 16 q^{65} + 4 q^{67} - 24 q^{69} - 16 q^{71} + 8 q^{73} - 8 q^{74} + 12 q^{75} + 8 q^{79} - 32 q^{80} - 92 q^{81} - 16 q^{84} + 32 q^{86} + 4 q^{89} - 48 q^{90} - 4 q^{91} - 24 q^{92} - 32 q^{95} - 32 q^{96} - 16 q^{97} - 48 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 8 * q^4 + 8 * q^5 + 8 * q^6 - 16 * q^10 + 8 * q^12 - 8 * q^13 - 16 * q^16 - 24 * q^18 - 16 * q^20 + 8 * q^21 + 12 * q^23 + 32 * q^27 + 8 * q^29 + 32 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^37 - 32 * q^38 - 24 * q^45 + 24 * q^46 + 12 * q^47 + 16 * q^48 - 24 * q^50 + 8 * q^51 + 16 * q^52 + 64 * q^54 + 24 * q^57 - 16 * q^58 - 8 * q^61 + 16 * q^62 - 16 * q^63 + 32 * q^64 - 16 * q^65 + 4 * q^67 - 24 * q^69 - 16 * q^71 + 8 * q^73 - 8 * q^74 + 12 * q^75 + 8 * q^79 - 32 * q^80 - 92 * q^81 - 16 * q^84 + 32 * q^86 + 4 * q^89 - 48 * q^90 - 4 * q^91 - 24 * q^92 - 32 * q^95 - 32 * q^96 - 16 * q^97 - 48 * q^98 - 16 * q^99

Introduction

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